I think I am having a software problem with the mouse driver or another software problem.
When I turn on the computer the keyboard will work until the Windows desktop comes up. The computer will then refuse to process keyboard strokes or mouse movements or clicks if I have the PS2 mouse plugged in. It is a standard 2 button mouse without a scroll wheel or anything else, and as far as I can tell, mouse.drv is the driver that is being used.
When I start the system without the mouse plugged in the keyboard will work just fine.
The problem is NOT with the mouse (I checked), and I highly doubt that there is anything wrong with the motherboard. I do not plug in or remove the mouse or keyboard while the computer is on.
This problem happened once before and I can't remember what I did to fix it. Navigating with the keyboard only isn't fun, so please let me know if you have any ideas.

For shits and giggles:
(Read first before proceeding ;)
Shut down the computer, swap the positions of the keyboard and the mouse plugs (ie plug the mouse in where the keyboard is now, and vice versa), reboot. Report.

the computer giggled and then took a dump.
It didn't work. Windows loaded but pressing the caps lock key made the caps lock, number lock and scroll lock LEDs all light up. The windows key and tab key didn't work either. THe mouse is now unplugged and the purple keyboard plug is in the purple jack.
When the mouse is plugged in the keyboard responds normally (repeatedly pressing the caps lock key causes the caps lock LED to light up and turn off) right until the icons are displayed on the desktop. Then keystrokes stop being processed.

I am not really in a position to try another keyboard (just moved into town) and am poor.
Buy a mac - there's an idea. My parents are still running a IIsi - 1990 vintage. Dad uses it because it doesn't crash.
Thanks for the suggestions everyone!

Steps I would try:
New keyboard. These are cheap. Look for a used one, less then $15 bucks easy.
Then reload windows.
If that doesn't work, it may be your motherboard.
-legrue
edited to add.
Oh, if you want, you can try an old serial mouse if your serial port is available.

Alright, you people are pissing me off.
First of all, buying a MAC would be a good idea of you like to say you have a computer.
Now if you actually need to use it and run some software, stick with your PC clone.
2nd of all, if your not willing to buy a new keyboard or other hardware to fix the issue, we might as well delete this thread then.
That's like your car blowing a f'in tire, and you sitting on the side of the road saying, well what do I do next.
Ummm buy a new tire.
You can't afford a new tire?
O ok, have fun on the side of the road.
Use some common sense buddy, geez.

This reminds me of my favorite comedy radio show: The Jeff Levy show for PC users. If any of you MacUsers out there want a real fun treat, listen to Jeff. Often his solutions to problems begin like this "Okay, if rebooting doesn't work...now get a pencil and paper a write this down... type A dot dot backslash...blah blah blah..."
It just cracks me up!